The Advanced X-ray Imaging Satellite (AXIS) is a Probe-class concept that will build on the legacy of the Chandra x-ray Observatory by providing low-background, arcsecond-resolution in the 0.3-10 keV band across a 450 arcminute2 field of view, with an order of magnitude improvement in sensitivity. AXIS utilizes breakthroughs in the construction of lightweight segmented x-ray optics using single-crystal silicon, and developments in the fabrication of large-format, small-pixel, high readout rate CCD detectors with good spectral resolution, allowing a robust and cost-effective design. Further, AXIS will be responsive to target-of-opportunity alerts and, with onboard transient detection, will be a powerful facility for studying the time-varying x-ray universe, following on from the legacy of the Neil Gehrels (Swift) x-ray observatory that revolutionized studies of the transient x-ray Universe. In this paper, we present an overview of AXIS, highlighting the prime science objectives driving the AXIS concept and how the observatory design will achieve these objectives.